CN119277424A - Downlink beamforming method for decellularized mMIMO system based on non-ideal calibration - Google Patents
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Abstract
本发明公开了一种基于非理想校准去蜂窝mMIMO系统的下行波束方法，该方法首先基于莱斯衰落信道模型，给出了非理想校准下上行信道与下行信道之间的映射关系，然后根据非理想校准条件下下行用户接收的数据表达式，推导了去蜂窝大规模MIMO系统的下行速率表达式，最后，以最大化下行和速率为目标，利用拉格朗日对偶变换方法和放缩式交替方向乘子法迭代求解下行和速率最大化优化问题，得到了最优下行波束序列。本发明减轻了互易性校准误差对系统性能的负面影响，降低了非理想校准导致的性能损失，有效提升了非理想校准下去蜂窝大规模MIMO系统的下行速率。
The present invention discloses a downlink beam method for a decellularized mMIMO system based on non-ideal calibration. The method first gives a mapping relationship between uplink channels and downlink channels under non-ideal calibration based on the Rice fading channel model, and then derives the downlink rate expression of the decellularized large-scale MIMO system according to the data expression received by the downlink user under non-ideal calibration conditions. Finally, with the goal of maximizing the downlink sum rate, the Lagrange dual transformation method and the scaled alternating direction multiplier method are used to iteratively solve the downlink sum rate maximization optimization problem, and the optimal downlink beam sequence is obtained. The present invention reduces the negative impact of reciprocity calibration errors on system performance, reduces the performance loss caused by non-ideal calibration, and effectively improves the downlink rate of the decellularized large-scale MIMO system under non-ideal calibration.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a downlink beam method for a cellular mMIMO system based on non-ideal calibration.
Background
In recent years, as a derivative technology of coordinated multipoint cooperative communication, a cellular-removing massive MIMO technology has been widely studied. On the one hand, the cellular network abandons the cell concept in the cellular architecture, and by disposing a large number of Access Points (APs) around users, the communication distance between the APs and the users is greatly shortened, the path loss of signal propagation is reduced, and inter-cell interference and handover caused by cell division are avoided. On the other hand, due to the introduction of the massive MIMO technology, by configuring a plurality of antennas or antenna arrays at the AP, a higher macro diversity gain is provided for the whole system, and in addition, as the number of antennas increases, the channel hardening and the advantageous propagation effects are more remarkable, in which case, the cellular massive MIMO system can obtain a higher communication capacity and a better service quality even if a simpler signal receiving scheme is adopted.
In wireless communication, channel state information is important for the whole communication process, which determines the quality of signal detection and reception. In general, uplink channel information can be estimated by a channel estimation method, such as channel blind estimation and pilot transmission based estimation, and downlink channel information can be directly given by uplink channel estimation by utilizing channel reciprocity characteristics of a time division duplex mode, so that current research on a de-cellular massive MIMO system assumes that the system works in the time division duplex mode to reduce channel estimation operation. However, the transceiver radio frequency links of the AP and the ue are two independent circuits, and the frequency response of the transceiver fluctuates randomly due to the random effect of the thermal noise of the circuits, so that the channel reciprocity cannot be established in the actual system, and the uplink and downlink channels cannot be considered to be completely equal. Although some existing reciprocity calibration methods can improve the problems, the existing calibration methods rely heavily on the characteristics of channel estimation to cause residual errors in the calibration process, so that uplink and downlink channel mismatch is caused, and further, the design accuracy of downlink beams is reduced, and the downlink communication rate is seriously reduced. In this context, the present invention proposes a downstream beam method based on a non-ideal calibration of the cellular mMIMO system.
Disclosure of Invention
The invention aims to provide a downlink beam method for calibrating a cellular mMIMO system based on non-ideal, which is used for reducing the influence of calibration errors and improving the downlink speed by designing a downlink beam sequence on the basis of considering residual errors caused by the non-ideal calibration process.
In order to achieve the above purpose, the technical scheme of the invention is as follows, the downlink beam method for calibrating the cellular mMIMO system based on non-ideal calibration comprises the following steps:
step 1, based on a honeycomb-removed large-scale MIMO system under a non-ideal calibration condition, giving out a functional relation between an uplink channel and a downlink channel by considering errors in the reciprocity calibration process of the uplink channel and the downlink channel;
step 2, based on the functional relation and the rice fading channel model, giving a data expression received by a user in a downlink stage, and deducing a downlink rate expression;
step 3, based on a downlink rate expression, using downlink and rate as objective functions, and providing a downlink and rate maximization problem of the AP with power constraint;
and 4, reconstructing an original optimization problem by using a Lagrange dual conversion method, and then performing iterative solution on the reconstruction problem by using a scaled alternate direction multiplier method so as to output an optimal downlink beam sequence.
Further, in step 1, the functional relationship between the uplink and downlink channels is:
,
,
Wherein, Represent the firstAP and thA sequence of downlink channels between the individual users,Represent the firstAP and the firstThe sequence of uplink channels between individual users,Represent the firstThe frequency response mismatch coefficients of the individual users,Represents calibrated firstThe frequency response mismatch coefficients of the individual users,Represent the firstCalibration errors of the frequency response mismatch coefficients of the individual users,Represent the firstThe frequency response mismatch coefficient matrix of each AP,Represents calibrated firstThe frequency response mismatch coefficient matrix of each AP,Represent the firstCalibration error matrix for the frequency response mismatch coefficients of the APs.
Further, through the uplink channel estimation process, the uplink channel includes two parts of uplink channel estimation and estimation error, where the downlink channel is expressed as
Wherein, Represent the firstAP and thThe sequence of uplink channel estimates between individual users,Represent the firstAP and thUplink channel estimation error sequences between individual users,Represent the firstAP and thA sequence of downlink channel estimates between individual users,Represent the firstAP and thDownlink channel estimation error sequences between individual users.
Further, in step 2, the user receives data in the downlink stageThe expression of (2) is:
Wherein, The total number of APs is indicated,The total number of users is indicated,Representing the normalized downlink data transmission signal-to-noise ratio,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstData symbols of individual users, which satisfyAnd is also provided with,Represent the firstThe data symbols of the individual users are transmitted,Represent the firstThe additive complex gaussian random noise received by each user has a mean value of 0, a variance of 1,Represent the firstAP and thA sequence of downlink channel estimates between individual users,Represent the firstAP and thA sequence of downlink channel estimation errors between individual users,Represents the operation of conjugate transposition,The expression of the conjugate operation is given,Representing a desired operation.
In step 2, the derived firstThe downlink rate expression for each user is:
Wherein, Represent the firstThe signal-to-interference-and-noise ratio of the individual users,Indicating all APs and the thA sequence of downlink channel estimates between individual users,Indicating all APs and the thA sequence of downstream beams between the individual users,Indicating all APs and the thDownstream beam sequence, matrix between individual users,
Indicating all APs and the thDownlink channel estimation error sequence, matrix between individual users,Indicating all APs and the thA sequence of downlink channel estimation errors between individual users,Representing a transpose operation.
Further, in step 3, the downlink and rate maximization problem is expressed as:
Wherein, Representing the euclidean norm square.
Further, in step 4, the objective function is reconstructed by using the lagrangian dual transform method as follows:
Wherein, AndRepresenting the sequence of auxiliary variables introduced.
In step 4, the reconstruction problem is expressed as:
。
Further, in step 4, the optimization problem is solved iteratively by using a first-order condition and a scaling alternate direction multiplier method, and the specific steps are as follows:
Step 4-1, based on the first order condition, letting the objective function Respectively aboutAndThe first order partial derivative function of (2) is equal to 0, and the obtained
,
Wherein, AndRespectively in each iterationAndIs used for the optimal solution of (a),
Step 4-2, based on the scaled alternate direction multiplier method, the lagrangian augmentation function of the reconstruction problem can be expressed as:
Wherein, An indication function representing the AP power constraint,Representation ofIs used for the sequence of auxiliary variables,Representing the scaled sequence of dual variables,A penalty factor is indicated and is indicated,
Step 4-3, at the firstIn several iterations, for a given valueAndBased on the first order condition, let the functionWith respect toIs equal to 0, all APs and the first order partial derivative function of (c)Downstream beam sequence between individual users at the firstThe expressions in the iterations are expressed as
Wherein,
,Representing dimensions asIs used for the matrix of units of (a),For the number of antennas per AP,
Step 4-4, giveAndBased on KKT condition, solving the following sub-problems
ObtainingIn the first placeThe expression in the iteration is
Wherein, ,
Step 4-5, giveAndDual variableIn the first placeThe expressions in the multiple iterations are updated to
Step 4-6, repeating steps 4-1 to 4-5 until the downlink and the velocity converge, ending the circulation and outputting the downlink beam optimal scheme, namely,Finger numberAP and the firstOptimal beam sequences between individual users.
An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the non-ideal calibration-based downstream beam method to cellular mMIMO system when the program is executed.
Compared with the prior art, the invention has the beneficial effects that:
(1) The present invention considers the imperfect channel reciprocity and the residual error caused by the imperfect calibration, which is a non-negligible performance influencing factor for the actual design of the wireless communication system, thereby making the present invention have more practical significance;
(2) According to the invention, on the basis of a non-ideal calibration honeycomb-removed large-scale MIMO system, a Lagrange dual conversion method and a scaling alternate direction multiplier method are combined for the first time to design a downlink beam sequence of the system, so that the performance loss degree caused by calibration errors is reduced, and the technical problem which is not solved by most of the existing works is solved;
(3) The method has the advantages of low calculation complexity, less needed iteration times and high convergence speed, thereby having higher feasibility.
Drawings
FIG. 1 is a graph of cumulative distribution function of downstream rate for different downstream beam methods;
fig. 2 is a chart of the iteration number of the downstream beam design method.
Detailed Description
The technical means and effects of the present invention will be further described with reference to the accompanying drawings, so that the present invention can be easily understood. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
The embodiment provides a downlink beam method for a cellular mMIMO system based on non-ideal calibration, which aims to reduce the deterioration of the system performance caused by the non-ideal calibration and improve the downlink rate. The method comprises the following steps:
step 1, based on a honeycomb-removed large-scale MIMO system under a non-ideal calibration condition, giving out a functional relation between an uplink channel and a downlink channel by considering errors in the reciprocity calibration process of the uplink channel and the downlink channel;
step 2, based on the functional relation and the rice fading channel model, giving a data expression received by a user in a downlink stage, and deducing a downlink rate expression;
step 3, based on a downlink rate expression, using downlink and rate as objective functions, and providing a downlink and rate maximization problem of the AP with power constraint;
and 4, reconstructing an original optimization problem by using a Lagrange dual conversion method, and then performing iterative solution on the reconstruction problem by using a scaled alternate direction multiplier method so as to output an optimal downlink beam sequence.
Further, the present invention contemplates a de-cellular massive MIMO system under non-ideal calibration conditions, the system comprisingAccess point APEach AP uses by a single antenna userA root antenna. Due to imperfect channel reciprocity, the functional relationship between the uplink and downlink channels is:
,
,
Wherein, Represent the firstAP and thA sequence of downlink channels between the individual users,Represent the firstAP and the firstThe sequence of uplink channels between individual users,Represent the firstThe frequency response mismatch coefficients of the individual users,Represents calibrated firstThe frequency response mismatch coefficients of the individual users,Represent the firstCalibration errors of the frequency response mismatch coefficients of the individual users,Represent the firstThe frequency response mismatch coefficient matrix of each AP,Represents calibrated firstThe frequency response mismatch coefficient matrix of each AP,Represent the firstCalibration error matrix for the frequency response mismatch coefficients of the APs.
Further, through the uplink channel estimation process, the uplink channel includes two parts of uplink channel estimation and estimation error, where the downlink channel is expressed as
Wherein, Represent the firstAP and thThe sequence of uplink channel estimates between individual users,Represent the firstAP and thUplink channel estimation error sequences between individual users,Represent the firstAP and thA sequence of downlink channel estimates between individual users,Represent the firstAP and thDownlink channel estimation error sequences between individual users.
Further, in step 2, the user receives data in the downlink stageThe expression of (2) is:
Wherein, The total number of APs is indicated,The total number of users is indicated,Representing the normalized downlink data transmission signal-to-noise ratio,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstData symbols of individual users, which satisfyAnd is also provided with,Represent the firstThe data symbols of the individual users are transmitted,Represent the firstThe additive complex gaussian random noise received by each user has a mean value of 0, a variance of 1,Represent the firstAP and thA sequence of downlink channel estimates between individual users,Represent the firstAP and thA sequence of downlink channel estimation errors between individual users,Represents the operation of conjugate transposition,The expression of the conjugate operation is given,Representing a desired operation.
In step 2, the derived firstThe downlink rate expression for each user is:
Wherein, Represent the firstThe signal-to-interference-and-noise ratio of the individual users,Indicating all APs and the thA sequence of downlink channel estimates between individual users,Indicating all APs and the thA sequence of downstream beams between the individual users,Indicating all APs and the thDownstream beam sequence, matrix between individual users,
Indicating all APs and the thDownlink channel estimation error sequence, matrix between individual users,Indicating all APs and the thA sequence of downlink channel estimation errors between individual users,Representing a transpose operation.
Further, taking the downlink and the rate as objective functions, considering that each AP has a maximum power limit, the downlink and rate maximization problem is expressed as:
Wherein, Representing the euclidean norm square.
Further, to separate the signal-to-interference-and-noise ratio function from the logarithmic function, an auxiliary variable is introducedAndReconstructing an objective function into a binary conversion method by utilizing a Lagrangian method:
Wherein, AndRepresenting the sequence of auxiliary variables introduced.
Further, the original objective function is replaced by a reconstruction function, and the reconstruction problem of the original optimization problem is expressed as:
furthermore, the reconstruction problem is solved iteratively by using a first-order condition and a scaled alternative direction multiplier method.
Step 4-1, based on the first order condition, letting the objective functionRespectively aboutAndThe first order partial derivative function of (2) is equal to 0, and is obtained by solving
,
Wherein, AndRespectively in each iterationAndIs used for the optimal solution of (a),
Step 4-2, based on the scaled alternate direction multiplier method, the lagrangian augmentation function of the above reconstruction problem can be expressed as:
Wherein, An indication function representing the AP power constraint,Representation ofIs used for the sequence of auxiliary variables,Representing the scaled sequence of dual variables,A penalty factor is indicated and is indicated,
Step 4-3, at the firstIn several iterations, for a given valueAndBased on the first order condition, let the functionWith respect toIs equal to 0, all APs and the first order partial derivative function of (c)Downstream beam sequence between individual users at the firstThe expressions in the iterations are expressed as
Wherein,
,Representing dimensions asIs used for the matrix of units of (a),Step 4-4, given the number of antennas per APAndBased on KKT condition, solving the following sub-problems
ObtainingIn the first placeThe expression in the iteration is
Wherein, ,
Step 4-5, giveAndDual variableIn the first placeThe expressions in the multiple iterations are updated to
Step 4-6, repeating steps 4-1 to 4-5 until the downlink and the velocity converge, ending the circulation and outputting the downlink beam optimal scheme, namely,Finger numberAP and the firstOptimal beam sequences between individual users.
Further, substituting the obtained optimal downlink beam sequence into a downlink rate expression, and calculating the downlink rate of each user.
Referring to fig. 1, it can be found that, when the ordinate is equal to 0.5, the corresponding downlink sum rate value is 51.60 (bit/s/Hz) in the ideal calibration, the downlink sum rate of the maximum ratio transmission scheme is 27.38 (bit/s/Hz) in the non-ideal calibration, and the downlink sum rate of zero-forcing precoding is 34.19 (bit/s/Hz), which are reduced by 46.94% and 33.74% respectively compared with the ideal calibration, because the calibration error caused by the non-ideal calibration severely reduces the system performance. Under the same condition, the downlink and speed of the method is 37.63 (bit/s/Hz), which is 37.43% and 10.06% higher than the maximum ratio transmission and zero-forcing precoding, fully verifies that the beam design proposal provided by the method can effectively lighten the influence of calibration errors, make up the performance loss caused by non-ideal calibration and improve the system performance.
Referring to fig. 2, it can be found that as the iteration number increases, the downlink and the rate gradually increase and converge, and even for a large-scale system, that is, the AP number is 80 and the user number is 30, the method of the present invention can still converge after about 4 iterations, which effectively illustrates that the method of the present invention has better feasibility.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (9)
1. A downstream beam method for calibrating a cellular mMIMO system based on non-idealities, the method comprising the steps of:
Step 1, based on a honeycomb-removed large-scale MIMO system under non-ideal calibration, giving out a functional relation between uplink and downlink channels by considering errors in the reciprocity calibration process of the uplink and downlink channels;
step 2, based on the functional relation and the rice fading channel model, giving a data expression received by a user in a downlink stage, and deducing a downlink rate expression;
step 3, based on a downlink rate expression, using downlink and rate as objective functions, and providing a downlink and rate maximization problem of the AP with power constraint;
and 4, reconstructing an original optimization problem by using a Lagrange dual conversion method, and then performing iterative solution on the reconstruction problem by using a scaled alternate direction multiplier method so as to output an optimal downlink beam sequence.
2. The downstream beam method based on the non-ideal calibration cellular mMIMO system as set forth in claim 1, wherein in step 1, the functional relationship between the upstream and downstream channels is:
,
,
Wherein, Represent the firstAP and thA sequence of downlink channels between the individual users,Represent the firstAP and the firstThe sequence of uplink channels between individual users,Represent the firstThe frequency response mismatch coefficients of the individual users,Represents calibrated firstThe frequency response mismatch coefficients of the individual users,Represent the firstCalibration errors of the frequency response mismatch coefficients of the individual users,Represent the firstThe frequency response mismatch coefficient matrix of each AP,Represents calibrated firstThe frequency response mismatch coefficient matrix of each AP,Represent the firstCalibration error matrix for the frequency response mismatch coefficients of the APs.
3. The method for downstream beam passing through non-ideal calibration cellular mMIMO system as in claim 1, wherein in step 2, the user receives data during the downstream phaseThe expression of (2) is:
Wherein, The total number of APs is indicated,The total number of users is indicated,Representing the normalized downlink data transmission signal-to-noise ratio,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstAP and the firstA sequence of downstream beams between the individual users,Represent the firstData symbols of individual users, which satisfyAnd is also provided with,Represent the firstThe data symbols of the individual users are transmitted,Represent the firstThe additive complex gaussian random noise received by each user has a mean value of 0, a variance of 1,Represent the firstAP and thA sequence of downlink channel estimates between individual users,Represent the firstAP and thA sequence of downlink channel estimation errors between individual users,Represents the operation of conjugate transposition,The expression of the conjugate operation is given,Representing a desired operation.
4. The method for downstream beam removal based on non-ideal calibration of a cellular mMIMO system as set forth in claim 1, wherein in step 2, the derived firstThe downlink rate expression for each user is:
Wherein, Represent the firstThe signal-to-interference-and-noise ratio of the individual users,Indicating all APs and the thA sequence of downlink channel estimates between individual users,Indicating all APs and the thA sequence of downstream beams between the individual users,Indicating all APs and the thDownlink beam ordering between individual users
Column, matrix,
Indicating all APs and the thDownlink channel estimation error sequence, matrix between individual users,Indicating all APs and the thA sequence of downlink channel estimation errors between individual users,Representing a transpose operation.
5. The downstream beam method based on the non-ideal calibration cellular mMIMO system as claimed in claim 1, wherein in step 3, the downstream and rate maximization problem is expressed as:
Wherein, Representing the euclidean norm square.
6. The downstream beam method based on the non-ideal calibration cellular mMIMO system according to claim 1, wherein in step 4, the objective function is reconstructed by using the lagrangian dual transform method as:
Wherein, AndRepresenting the sequence of auxiliary variables introduced.
7. The downstream beam method based on the non-ideal calibration cellular mMIMO system as claimed in claim 1, wherein in step 4, the reconstruction problem is expressed as:
。
8. the method for performing downlink beam calibration on a non-ideal calibration cellular mMIMO system according to claim 1, wherein in step 4, the optimization problem is solved iteratively by using a first-order condition and a scaled alternate direction multiplier method, and the specific steps are as follows:
Step 4-1, based on the first order condition, letting the objective function Respectively aboutAndThe first order partial derivative function of (2) is equal to 0, and the obtained
,
Wherein, AndRespectively in each iterationAndIs used for the optimal solution of (a),
Step 4-2, based on the scaled alternate direction multiplier method, the lagrangian augmentation function of the reconstruction problem is expressed as:
Wherein, An indication function representing the AP power constraint,Representation ofIs used for the sequence of auxiliary variables,Representing the scaled sequence of dual variables,A penalty factor is indicated and is indicated,
Step 4-3, at the firstIn several iterations, for a given valueAndBased on the first order condition, let the functionWith respect toIs equal to 0, all APs and the first order partial derivative function of (c)Downstream beam sequence between individual users at the firstThe expression in the multiple iterations is expressed as:
Wherein,
,Representing dimensions asIs used for the matrix of units of (a),For the number of antennas per AP,
Step 4-4, giveAndThe following sub-problems are solved based on the KKT condition,
ObtainingIn the first placeThe expression in the iteration is
Wherein, ,
Step 4-5, giveAndDual variableIn the first placeThe expressions in the multiple iterations are updated to
Step 4-6, repeating steps 4-1 to 4-5 until the downlink and the velocity converge, ending the circulation and outputting the downlink beam optimal scheme, namely,Finger numberAP and the firstOptimal beam sequences between individual users.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the program, implements a non-ideal calibration-based downstream beam method for a cellular mMIMO system as claimed in any one of claims 1 to 8.
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